I need a help to solve the question regarding normal distribution. The question is :
If X and Y are standard normal distribution and are independent then how to find the pdf and mgf of XY?

Nov 13th 2012, 09:17 AM

abender

Re: Suman Thapa

The (univariate) normal PDF is given by .

When is standard normal, , so that the standard normal PDF is .

is also a standard normal random variable, so its PDF is similarly .

Now, If and are INDEPENDENT, then .

So, .

Nov 13th 2012, 09:42 AM

sumanthapa

Re: Suman Thapa

Thanks for the solution. But I mean, if Z = XY (product of X and Y), where X and Y are standard normal distribution, then how to find the pdf and moment generating function(mgf) of Z? Could you please help me? Thanks.